The formula for Heisenberg's uncertainty principle is

Options

A. `lambda = ( h)/( mv)`
B. `Deltax xx Deltap ge ( h)/( 4pi)`
C. `Deltax xx Deltap ge ( h)/( 2pi)`
D. `mvr = n (h)/(2pi)`

Answer

**Step-by-Step Solution:**

1. **Understanding Heisenberg's Uncertainty Principle**: The Heisenberg's uncertainty principle states that it is impossible to simultaneously know both the position and momentum of a particle with absolute precision. This principle is fundamental in quantum mechanics.

2. **Identifying the Variables**: In the context of the uncertainty principle:
- \( \Delta x \) represents the uncertainty in position.
- \( \Delta p \) represents the uncertainty in momentum.

3. **Writing the Mathematical Expression**: The mathematical expression for Heisenberg's uncertainty principle is:
\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]
where \( h \) is Planck's constant.

4. **Analyzing the Options**: The given options are:
- a) \( \lambda = \frac{h}{mv} \) (De Broglie wavelength)
- b) \( \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \) (Correct)
- c) \( \Delta x \cdot \Delta p \geq \frac{h}{2\pi} \) (Incorrect)
- d) \( mv = \frac{nh}{2\pi} \) (Quantization of angular momentum)

5. **Selecting the Correct Answer**: Based on the analysis, option b) \( \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \) is the correct formula for Heisenberg's uncertainty principle.

**Final Answer**: The formula for Heisenberg's uncertainty principle is \( \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \).

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